Version 3.0 (5 October 1997): third draft; changes in section 6 proposed
by Cheymol and Kaufman.

Version 3.1 (26 October 1997): main modification: change of lowest
Elo to 1 rather than 500.

Version 3.2 (28 November 1997): formulation issues resolved.

Version 4.0 (26 July 1998): promotion issues and rating calculation
for unrated/provisional players resolved. This draft to be presented to
FESA and SFA for feedback.

3. Background

Five years ago John Kenney and I made a first pass at establishing a
correspondence table between dan/kyu grades and Elo ratings. Our ultimate
goal was to produce a promotion system based on Elo ratings as the (then
and now) current point system that I had devised is inflationary by its
very nature. This is one of the reasons Europe has so many 3-dans and relatively
few 1- and 2-dans. The European correspondence table, also has a serious
problem with compression of grades as will become clear in section 5. In
America, over the past years Larry Kaufman has designed an integrated system
that relates grades to ratings and rating differences to handicaps. It has
proven to be very stable. Statistical analysis of the limited amount of
data available seems to indicate that the correspondence between handicap
and rating difference is the same for all strengths. The rating officers
on both sides of the Atlantic (Larry Kaufman and Eric Cheymol) and I think
the time is ripe to establish an integrated system so that a player's rating
and grade mean exactly the same no matter on which continent he plays. I
am involved in this matter as I have knowledge of and experience with both
the European and the American systems and because unifying the two is a
long-standing wish of mine. Considering that calculation of Elo ratings
on both sides of the ocean is done almost identically, the potentially highest
hurdle to unification has already been taken care of. Larry, Eric and I
(as well as Hans Secelle, Reijer Grimbergen and George Fernandez) have discussed
the issues extensively and this document is the result of these discussions.

4. Tournament practices

One requirement for arriving at a unified system is that tournament practices
on either side of the Atlantic are accepted by the other side. This proposal
does not aim to change these practices or impose new rules. There
are differences in minimum time allotment that make games ratable (i.e.,
valid for rating calculations). In Europe this is 45 minutes plus byoyomi,
in America 20 minutes plus byoyomi. This proposal does not intend to change
these regulations; both sides need only accept that these differences exist
and agree that they do not interfere with establishing reliable ratings.
Of course, FESA might decide to regard games ratable if the time limits
are 20 minutes+30 seconds, while recommending 45+30 in general and imposing
60+30 for Grand Prix tournaments. In America handicap games are an integrated
part of the rating system. Again, the intention of this proposal is not
that FESA accepts handicap games as ratable in European tournaments, but
only that regarding handicap games as ratable in America does not preclude
a unified rating system. It would be preferred if these differences disappeared
over time, but this is not a requirement for the present purpose of establishing
a single rating system. A unified rating system would also enable us to
have a single pan-atlantic rating list, but again this is not a necessity.
For all practical purposes it is easier to maintain two separate lists as
long as the rating of few players that appear on both lists is the same
on both lists.

5. Relationship between Elo ratings, dan/kyu
grades and handicaps

The Elo rating is the primary indicator of current actual strength, while
the dan and kyu grades are titles based on historic peak performances (much
like Grand Master, Master and FIDE Master titles in chess). When unifying
the current ratings systems, establishing the relationship between Elo ratings
and dan/kyu grades is of crucial importance. I will focus on the European
situation as the American system is already being brought in line with the
system proposed here (see Table I). In Europe in 1992, the Elo difference
between average 3- and 4-dans was 145 points; it was 125 on the average
for all dan grades. Nowadays, the "theoretical" Elo difference
between two subsequent dan grades is 100 points. This indicates that the
European grades are too close together in terms of the number of Elo points
that separates them. Based on the following observations, Eric Cheymol and
I have come to the conclusion that this is indeed the case.

A) In Japan some clubs distinguish between weak and strong 1 dans, 2
dans, 3 dans, and 4 dans. With an Elo difference of only 100 between grades,
it is virtually impossible to distinguish between weak and strong players
of the same dan grade. Also, European 1-dans and 2-dans have good chances
to beat a 3-dan. In Japan, a 1-dan would hardly ever beat a 3-dan if they
both received their grades in the same club. Therefore, it seems logical
to widen the ranges of Elo ratings that correspond to each dan grade.

B) European kyu and lower dan grades are probably at least 1 grade "harder"
than the average Japanese. Assuming that 4-dans/top 3-dans in Europe and
Japan are approximately of equal strength, this indicates that the Elo
range for each grade below 4-dan is too narrow.

C) Based on his personal experience with playing in Japan, Larry Kaufman
believes that 200 Elo points per dan grade is on the conservative side
for Japan: the range is probably about 225-250 there and certainly larger
than the 100 points now used in Europe. Since America uses 200 points,
it seems reasonably to compromise and use 150 points for the lower dan
grades.

D) The 2-dan and 1-dan populations in Europe (9 and 11, respectively)
each are about half the size of the 3-dan population (17). Also, the actual
average ratings for the lower dan grades are systematically lower than
the "theoretical" ratings (see Table I). These two observations
again indicate that the Elo ranges for the lower dan grades are too narrow.

Taking the above considerations into account and using the divider between
3-dan and 4-dan (2120 in Europe; 2100 in America) as an anchoring point,
the pan-atlantic correspondence detailed in Table I is proposed. It follows
the European system in that going from 3-dan to 15-kyu the Elo range per
grade becomes progressively narrower (pan-atlantic: 200, 150, 100; European:
100, 80, 60, 40). It remedies the problems with the overall too narrow European
ranges (as exemplified by items A-D above). Compared to the present European
system, it doubles the width of the ranges for the higher dan-grades (4-dan
and above). This brings them more in line with Japan and avoids inflation
of these higher grades by making it more difficult to break through into
the 5/6-dan grades (which are not awarded in Europe (yet?)). With 150 rather
than 200 Elo points for the lower dan grade ranges, the system should still
lead to grades that are "harder" than the Japanese. Promotion
to 1-dan and 1-kyu should be more difficult than promotion within the other
kyu grades; the proposed system adequately addresses this by making the
1 and 2-kyu Elo range appropriately wide (150 points).

Table I. Elo rating - dan/kyu grade correspondence

Grade

Elo rating

Europe

America

Proposed pan-atlantic

"theoretical"

average *

range

width

6-dan

2320 - 2419

--

2500 - 2699

2500 - 2699

200

5-dan

2220 - 2319

--

2300 - 2499

2300 - 2499

4-dan

2120 - 2219

2159 (8)

2100 - 2299

2100 - 2299

3-dan

2020 - 2119

1978 (17)

1900 - 2099

1900 - 2099

2-dan

1920 - 2019

1869 (9)

1700 - 1899

1750 - 1899

150

1-dan

1820 - 1919

1794 (11)

1500 - 1699

1600 - 1749

1-kyu

1740 - 1819

1694 (16)

1400 - 1499

1450 - 1599

2-kyu

1680 - 1739

1575 (9)

1300 - 1399

1300 - 1449

3-kyu

1620 - 1679

--

1200 - 1299

1200 - 1299

100

4-kyu

1560 - 1619

1435 (8)

1100 - 1199

1100 - 1199

5-kyu

1500 - 1559

1353 (4)

1000 - 1099

1000 - 1099

6-kyu

1440 - 1499

1375 (6)

900 - 999

900 - 999

7-kyu

1380 - 1439

1392 (2)

800 - 899

800 - 899

8-kyu

1320 - 1379

--

700 - 799

700 - 799

9-kyu

1260 - 1319

--

600 - 699

600 - 699

10-kyu

1200 - 1259

1182 (7)

500 - 599

500 - 599

11-kyu

1160 - 1199

--

400 - 499

400 - 499

12-kyu

1120 - 1159

1212 (3)

300 - 399

300 - 399

13-kyu

1080 - 1119

1173 (2)

200 - 299

200 - 299

14-kyu

1040 - 1079

--

100 - 199

100 - 199

15-kyu

1000 - 1039

1224 (3)

1 - 99

1 - 99

* Average of the July 1997 Elo list (numbers of players in parentheses).
-- indicates 0 or 1 players.

Since overall the Elo ranges are widened in the proposed system, a one-time
adjustment of ratings is appropriate. If this were not done, the rating
of many lower kyu players would correspond to a grade that is 4 or 5 levels
higher then their present one. The following adjustment addresses that issue
adequately:

The consequences of these adjustments for the present population would
be that:

Several 1-kyus and a few 1-dans have good chances for promotion in
the foreseeable future.

4 and 3-dan grades have become "harder" in that promotion
to these grades seems more difficult within the proposed system than with
the FESA point system. Within the point system players could obtain 3-dan
promotion by scoring points against 3-dans, who according to their Elo
rating perform below that grade. In fact, the inflationary nature of the
point system is the main reason for the relatively very large 3-dan population.
This indicates very strongly that the point system as a mechanism for promotion
should be replaced for dan players if not for the entire population.

On average all kyu players better than 9-kyu will end up in an Elo
bracket one level higher than their present grade. Also, the entire range
of kyu-grades from 1 to 15-kyu will be populated.

Although the total Elo range has widened (the lowest rating now being
1 rather than 1000), new players will rise through the ranks (=grades)
faster as the rating differences between them and their opponents are typically
three times as large as in the present system, while the Elo range of each
kyu grade has only doubled. This will prove quite stimulating for newcomers.

Table II. Handicap - Elo rating difference (DElo)
correspondence

handicap

DElo

handicap

DElo

sente

25

3 p (right Lance)

675

Lance

75

3 p (left Lance)

700

Bishop

225

4 p

750

Rook

300

5 p (right kNight)

900

Rook + Lance

400

5 p (left kNight)

1050

2 p

600

6 p

1200

When computing the rating difference between opponents in a handicap
game for rating calculations, the above handicap values are added to the
rating of the handicap receiver first. Thus, if a player rated 1800 gives
Bishop (225 points) to a player rated 1600, the game will be rated as if
the 1600 player were 25 points higher rated (1600+225=1825) than the 1800
player.

Larry Kaufman has carried out a careful statistical analysis of a large
number of games in terms of actual Elo rating differences, handicaps used
and the outcome of the games. On the basis of that analysis and the grade-rating
correspondences of table I, he proposes the system detailed in Table II
for relating handicaps to Elo rating differences. As said before, this handicap
system does not need to be adopted by FESA, but it might be advantageous
to introduce it e.g. in clubs where handicap games are often played. This
would help establishing fairly reliable ratings quickly even for players
who do not often play in tournaments and also in cases where large differences
in strength exist between players within a club.

In order to avoid drift of the population as a whole, every year the
ratings of all active players with a rating of 1900 or above and at least
fifty rated games are recorded, and one year from that moment the average
of those of them that are still active is compared to their previous year's
average. If any year's average is significantly lower than the previous
year's average, the rating officers by unanimous agreement may raise the
average rating of all players by an amount not to exceed the calculated
difference. These calculations are carried out on the basis of ratings,
not of grades.

6. Elo calculation and promotion based on Elo
ratings

The following consensus rules and regulations governing Elo rating determination
and promotions based on these ratings are being proposed.

6A) Gaining and losing Elo points

The FIDE "Logistic" Elo rating calculation formula (explained
in the "Official Laws of Chess"), that is currently used to calculate
European ratings, will be adopted without any changes. It relates a player's
rating gain or loss (DElo
in the formula below) upon completion of a tournament to the results of
his games and the difference in ratings between him and his opponents:

where the summation extends over all games this player played in the
tournament, V(i) is the result of the game against his i-th opponent (1
for a win, 0.5 for a draw, 0 for a loss), Elo(i) the rating of his i-th
opponent, Elo his own rating before the tournament, and K a coefficient
that, when divided by 2, indicates how many points a player gains (loses)
when winning (losing) against a player of the same rating. A K-value of
20 is adequate for the higher dan grades, but lower graded players that
can progress rapidly should be able to move faster, which the value of 40
enables them to do.

Table III. K-values and numbers of games required for promotion

grade range

Elo range

K-value

#games*

4-dan ... 6-dan

2100 - 2699

20

16 (8)

1-dan ... 3-dan

1600 - 2099

24

14 (7)

3-kyu ... 1-kyu

1200 - 1599

28

12 (6)

7-kyu ... 4-kyu

800 - 1199

32

10 (5)

11-kyu ... 8-kyu

400 - 799

36

8 (4)

15-kyu ... 12-kyu

1 - 399

40

6 (3)

* number of games above the lower bound required for promotion (number
of games above the midpoint are given in parentheses).

If a player with a rating below 1200 gains points in a "tournament",
his gain shall be doubled unless such doubling brings him over 1200. In
that case his new rating shall be 1200 or the rating he would have obtained
if his gain were not doubled (whichever is higher).

6B) Time table for calculation of Elo ratings on the basis of tournament
results

Events are to be rated in order of their finishing date if at all possible.
Therefore, an event should not be rated if the results of a prior event
have not yet been received.

For purposes of the rating system, a "tournament" is defined
as all games which are to be rated at one time, using the same starting
rating. If multiple events are held in a short time, they may all be rated
as if they were part of one large tournament.
No "tournament" can include more than twenty games by any one
player. If necessary to avoid this, an event will be broken into two or
more parts for rating purposes.

Club events are rated based on the date of the last game of the event.
It is recommended that any event that takes a long time (e.g. more than
4 months), at the discretion of the club running the event, be split into
two or more portions for rating purposes.

A tournament is ratable if at least two (provisional or established,
see section 6C below) rated players participate. Once a "tournament"
is rated, the new ratings will be used for subsequent events. The present
European custom of using the semi-annual rating as the basis for all events
over the next six months will be discontinued.

6C) Elo categories and procedure for rating tournaments

A player with less than 4 games is unrated. A player gets a provisional
rating after 4 games and an established rating after 15 games. A rating
remains in effect for an inactive player even if it is no longer published,
unless unusual circumstances indicate that it would be more accurate to
treat the player as a newcomer. A player who earns a club grade (either
in a western club or in Japan) from unrated play that is more than a grade
above the grade corresponding to his current rating and who has not played
a rated game for at least one year may have his rating redetermined at the
discretion of the rating officer. In that case, he will be regarded an unrated
player with two games assumed at his new grade (see section 6C1 below).

When rating a tournament first the unrated players are rated, then the
players with a provisional ratings and finally the established players:

The initial performance rating of unrated players is determined
on the basis of the PRE-event ratings of provisional and established players
(ignoring any games with other unrated players). This is done using the
Logistic formula of section 6A, with two stipulations:* if the player has no club grade, an assumed win and an assumed
loss are added to his score (example: 5-0 becomes 6-1). These "results"
are only added to a player's actual results to avoid the problem of perfect
scores having no defined value. They are removed from the record once a
player has a provisional rating and do not count towards getting an established
rating.* if the player has a club grade, he is assumed to have scored one
win and one loss against players rated in the middle of that grade. These
"results" are added to his actual results, remain on the record
and count towards getting an established rating.
Subsequently, the performance ratings of these unrated players are iteratively
recalculated with PRE-event ratings of provisional and established players
and current performance ratings of other unrated players until no change
occurs.

Using the Logistic formula of section 6A, the POST-event rating of
each provisional player is determined on the basis of his own PRE-event
rating, the PRE-event ratings of his established and provisional opponents
and the POST-event performance ratings of his unrated opponents. If N,
the number of rated games he has played (including the event being rated),
is less than twenty, the net gain or loss for the event is multiplied by
(20/N). This is not an iterative procedure.

Using the Logistic formula of section 6A, the POST-event rating of
each established player is determined on the basis of his own PRE-event
rating, the POST-event ratings of his unrated and provisional opponents
and the PRE-event ratings of his established opponents. Again, this is
not an iterative procedure.

This procedure gives provisional players fair POST-event ratings, but
more importantly it uses ratings that are as reliable as possible for the
calculation of POST-event ratings of established players.

6D) Determination of a promotion system based on Elo ratings

Promotion is an important issue: as demotions cannot occur, one must
be very careful when promoting players. As indicated in sections 3 and 5
above (and known even when it was introduced), the point system is by definition
inflationary. For example, a 1-dan with a 1923 rating is much stronger than
one with a 1678 rating, and this should be taken into account in any promotion
system. An Elo-based promotion system satisfies this condition.

Considering Elo ratings of European kyu players, it is clear that Elo
ratings and kyu grades hardly correlate. In fact, Dutch kyu grades used
to be "hard," but based on the current Elo list they seem "softer"
than most others. The practice of kyu promotions being awarded by individual
associations without any guiding principles has not worked and has led to
the present discrepancies between ratings and grades. Replacing the current
system of unregulated kyu grade assignments by an Elo-rating-based system
would solve that problem.

Based on these observations, we discourage use of the point system for
promotions and propose an Elo-based promotion system (for dan and kyu players
alike) instead. In this system, promotion to a certain grade requires that
a player satisfies one of the following three conditions:

he has had a rating above the lower bound rating corresponding
to that grade over the number of consecutive games shown in Table III.
This requirement is based on the system currently used in Europe. Examples:
if a 2-kyu has maintained a rating of 1450 or higher over 12 games, he
will be promoted to 1-kyu.

he has had a rating above the mid-point corresponding to that
grade over half the number of consecutive games that are required by condition
1 (shown in parentheses in Table III). This requirement is based on the
system currently used in America. Example: if an 11-kyu has maintained
a rating of 550 (500+100/2) or higher over 4 games, he will be promoted
to 10-kyu.

upon completion of any tournament, he has attained a rating corresponding
to the next higher grade. Example: a 2-kyu with a rating of 1750
(lower bound of 2-dan) or higher will be promoted to 1-dan (one can indeed
skip grades this way).

The numbers in Table III are chosen as a compromise between European
and American practices. Refer to section 6E for promotions to 5 and 6-dan.

Although new Elo ratings are calculated upon completion of an "event",
for purposes of promotion the ratings officers will keep track exactly after
which game a player

A) exceeded the lower-bound and mid-point ratings of the grades above
his current grade, and

B) has maintained those ratings during the number of consecutive games
listed in Table III (which earns him promotion).

For this reason it is very important that results of an event be reported
to the ratings officers in the actual playing order. If the actual order
in which games took place cannot possibly be determined, only then will
it be assumed that rating points were gained at a constant rate and an interpolation
scheme will be used to determine after which game a player crossed the promotion
threshold the first time (A) or when he has earned promotion by maintained
a rating above that threshold for enough consecutive games (B). The game
'thr' after which the threshold Elo(thr) was passed is given by:

where Elo(0) and Elo(end) are the Elo ratings at the beginning and end
of the event, respectively, while #games is the number of games making up
the event. This interpolation scheme should be avoided whenever possible,
though.

As mentioned in section 6A, new Elo ratings can and should be calculated
after each "event" or (mostly relevant for lower kyu players)
after each club night. This makes it convenient for national associations
and clubs to base promotions of their own players on Elo ratings. For an
Elo system and an Elo-based promotion system to be conveniently used in
tournaments and clubs alike, it is advantageous if a pan-atlantic shogi
pairing/Elo-calculation program become available for both PC and Macintosh.
It is proposed that this option be considered seriously by FESA and SFA.

6E) Promotion to 5 and 6-dan

Nihon Shogi Renmei (NSR) had asked foreign shogi organizations not to
award 5 or 6-dan promotions unless they were obtained in Japan. It is proposed
that neither European nor American organizations will promote a player to
5 or 6-dan at this point in time, unless the promotion is ratified by NSR.

* If a player has had a rating of 2300 (5-dan lower bound) for
16 consecutive games and his rating was above 2400 (5-dan mid-point) at
least once, NSR will be requested to ratify promotion to 5-dan.

* If a player has had a rating of 2500 (6-dan lower bound) for
16 consecutive games and his rating was above 2600 (6-dan mid-point) at
least once, NSR will be requested to ratify promotion to 6-dan.